Principles of fractals are described in the following publications:
1. Barnsley, M. F. and Berger, M. A., "Pictures Worth a Million Words", Projects in Scientific Computing, 1988-1989, Pittsburgh Supercomputing Center, 34-35. PA0 2. Barnsley, M. F., Berger, M. A. and Soner, H. M., "Mixing Markov Chains and their Images", Prob. Eng. Inf. Sci., 2(1988), 387-414. PA0 3. Berger, M. A., "Encoding Images Through Transition Probabilities", Mathl. Comput. Modelling, 11(1988), 575-577. PA0 4. Berger, M. A., "Images Generated by Orbits of 2-D Markov Chains", CHANCE 2(1989), 18-28. PA0 5. Berger, M. A., "IFS Algorithms for Wavelet Transforms, Curves and Surfaces, and Image Compression", Stochastic Models, Statistical Methods and Algorithms in Image Analysis, P. Barone et al., eds., Springer-Verlag, N.Y., 1991. PA0 6. Berger, M. A., "Random Affine Iterated Function Systems: Mixing and Encoding", Diffusion Processes and Related Problems in Analysis, Vol. 11: Stochastic Flows, M. Pinsky and Y. Wihstutz, eds., Birkhauser, Boston, 1991. PA0 7. Berger, M. A., "Random Affine Iterated Function Systems: Curve Generation and Wavelets", SIAM Review, 1992. PA0 8. Berger, M. A. and Soner, H. M., "Random Walks Generated by Affine Mappings", J. Theor. Prob. 1(1988), 239-264. PA0 Barnsley, M. F. and Hurd, L. P. "Fractal image compression", AK Peters, Ltd., Wellesley, Mass., 1993; PA0 Jacquin, A. E., "Image Coding Based on a Fractal Theory of Iterated Contractive Image Transformations", IEEE Trans. Image Proc. 1 (1992), 18-30; and PA0 Mazel, David S., "Fractal Modeling of Time-Series Data", Ph.D. Thesis, Georgia Institute of Technology, 1991.
Use of fractals for image compression is described by Barnsley and Sloan, of Iterated Systems, Inc. (ISI) in Norcross, Ga. The ISI method is described in U.S. Pat. Nos. 4,941,193 and 5,065,447.
Fractals and their applications are also described in the following publications: